If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP.

Solution

In the figure, PA and PB are two tangents from an external point P to a circle with centre O and radius = a

$∠ APB = 60 ° (given) \Rightarrow ∠ APQ = 30 ° (tangents are equally inclined to the line joining the point and the centre .) Now, OA ⊥ AP In right angled triangle OAP, \sin 30 ° = \frac{OA}{OP} \Rightarrow \frac{1}{2} = \frac{a}{OP} \Rightarrow OP = 2 a$

For Daily Free Study Material Join wiredfaculty

Circles

If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP.

Some More Questions From Circles Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction